Abstract: Mechanism for supporting and permitting selected adjustment of the position of a headrest relative to the back of a chair includes an elongate housing, support brackets pivotally connected adjacent opposite ends of the body, and a plurality of interleaved elongate plate members extending longitudinally of the body and movable relative thereto, with opposite ends of the interleaved plate members pivotally connected to the brackets. Clamping mechanism is provided for releasably clamping interleaved portions of the plate members to hold them, and their associated brackets, in selected positions. A slide mechanism mounts a headrest permitting translational movement of the headrest relative to the mechanism.